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Math Help - I need help with a homework question - Statistical Significance

  1. #1
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    Question I need help with a homework question - Statistical Significance

    The manufacturer of a daily dietary supplement claims that its product will help people lose weight. The company obtains a random sample of 950 adult males aged 20 to 74 who take the supplement and finds their mean weight loss after eight weeks to be 0.9 pounds. Assume the population standard deviation weight loss is 7.2 pounds.

    (a) State the null and alternative hypotheses.

    (b) Test the hypothesis at α = 0.1 level of significance. Is a mean weight loss of 0.9 pounds significant?

    (c) Do you think that a mean weight loss of 0.9 pounds is worth the expense and commitment of a daily dietary supplement? In other words, does the weight loss have any practical significance?

    (d) Test the hypothesis at α = 0.1 level of significance with n = 40 subjects. Assume that the sample mean weight loss is still 0.9 pounds. Is a sample mean weight loss of 0.9 pounds significantly more than 0 pounds? Conclude that large sample sizes cause P-Values to shrink substantially, all other things being the same.

    If someone could walk me or help me with this problem, it would be greatly appreciated! Thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    H_0:\mu=0 vs. H_a:\mu>0

    where \mu is the mean weight loss of anyone who takes this diet for 8 weeks.

    The test stat is  {\bar X-\mu_0\over\sigma/\sqrt{n}}={.9-0\over 7.2/\sqrt{950}}\approx 3.8527

    which is significant at alpha equal to .1
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